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// Copyright © 2026 Mikhail Hogrefe
//
// This file is part of Malachite.
//
// Malachite is free software: you can redistribute it and/or modify it under the terms of the GNU
// Lesser General Public License (LGPL) as published by the Free Software Foundation; either version
// 3 of the License, or (at your option) any later version. See <https://www.gnu.org/licenses/>.
use crate::natural_polynomial::NaturalPolynomial;
use malachite_base::num::arithmetic::traits::IsUnit;
impl IsUnit for NaturalPolynomial {
/// Determines whether a [`NaturalPolynomial`] is a unit: whether it is the constant polynomial
/// 1, the only polynomial with natural coefficients that has a multiplicative inverse.
///
/// No modulus is involved, as with [`IsUnit`] for [`Natural`](crate::natural::Natural). Modulo
/// $n$, every constant coprime to $n$ is also a unit, and so, when $n$ is composite, are some
/// polynomials of positive degree.
///
/// # Worst-case complexity
/// Constant time and additional memory.
///
/// # Examples
/// ```
/// use core::str::FromStr;
/// use malachite_base::num::arithmetic::traits::IsUnit;
/// use malachite_base::num::basic::traits::Zero;
/// use malachite_base::polynomial::Polynomial;
/// use malachite_nz::natural_polynomial::NaturalPolynomial;
///
/// assert_eq!(NaturalPolynomial::one().is_unit(), true);
/// assert_eq!(NaturalPolynomial::ZERO.is_unit(), false);
/// assert_eq!(NaturalPolynomial::two().is_unit(), false);
/// assert_eq!(NaturalPolynomial::x().is_unit(), false);
/// assert_eq!(NaturalPolynomial::from_str("x+1").unwrap().is_unit(), false);
/// ```
#[inline]
fn is_unit(&self) -> bool {
*self == 1u32
}
}